# Nonnegative matrix factorization

### From Wikimization

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then <math>Y\!=U^\star U^{\star\rm T}.</math> | then <math>Y\!=U^\star U^{\star\rm T}.</math> | ||

+ | <br> | ||

In summary, initialize <math>Y=I\,</math> then alternate solution of | In summary, initialize <math>Y=I\,</math> then alternate solution of | ||

## Revision as of 14:27, 28 September 2009

Example from Convex Optimization & Euclidean Distance Geometry, ch.4:

Given rank-2 nonnegative matrix

find a nonnegative factorization by solving

which follows from the fact, at optimality,

Use the known closed-form solution for a direction vector to regulate rank (rank constraint is replaced) by Convex Iteration;

set to an ordered diagonalization and , then

In summary, initialize then alternate solution of

with